Effect of fillers on the phase stability of binary polymer blends: A dynamic shear rheology study

Acta Materialia 53 (2005) 5117–5124 www.actamat-journals.com

Effect of fillers on the phase stability of binary polymer blends: A dynamic shear rheology study Yajiang Huang a, Sujun Jiang a, Guangxian Li

a,b,*

, Dahua Chen

a

a

b

College of Polymer Science and Engineering, Sichuan University, Chengdu 610065, PR China State Key Laboratory of Polymer Material and Engineering, Sichuan University, Chengdu 610065, PR China Received 3 March 2005; received in revised form 16 July 2005; accepted 22 July 2005 Available online 5 October 2005

Abstract The phase boundaries of untreated silica-filled and unfilled poly(methyl methacrylate) (PMMA)/poly(styrene-stat-acrylonitrile) (SAN) blends were determined by dynamic shear rheology. The Flory–Huggins interaction parameter was also calculated according to the determined phase diagram after taking into account the composition change of the mixture matrix due to the incorporation of filler. It was found that, in comparison with the unfilled PMMA/SAN blends, the phase separation temperature of the filled polymer blend was increased, and the thermodynamic interaction parameter was correspondingly decreased, suggesting that the phase stability of PMMA/SAN mixtures is enhanced by the incorporation of silica. A mechanism for this phenomenon was proposed based on the selective adsorption of PMMA chains on silica particles. The adsorption of high molecular weight fraction of PMMA chains onto the surface of silica particles would decrease the average molecular weight of PMMA in the bulk matrix that would favor the miscibility of PMMA/SAN blends in the matrix, therefore leading to the increase of the phase separation temperature of blends in the bulk. In addition, the adsorption of PMMA also changed the blend composition ratio in the bulk matrix, which would cause a complicated influence on the phase separation temperature too.
2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Phase stability; Dynamic shear rheology; Polymer blends; Fillers

1. Introduction The commonly used polymer materials are usually manufactured not only by mixing several different macromolecules, but also by incorporating certain solid ‘‘filler’’ particles into the materials, in order to improve the modulus, impact strength, appearance, conductivity, or flammability of the materials [1]. Despite the large scale of utility of these composite materials, there is little understanding of how the filler particles influence the phase stability of binary polymer blends, which is of practical significance because it determines the stability

*

Corresponding author. E-mail address: [email protected] (G. Li).

of these multiphase mixtures against macroscopic phase separation. Small angle light scattering (SALS) is the most widely used technique to study the phase behavior and explore the phase separation dynamics of polymer blends. The following conditions are a prerequisite for the validity of SALS: a large difference between the refractive indices of components, and good transparency of the sample. However, polymer composites are generally opaque due to the incorporation of fillers. The substrate supporting the SALS thin samples may also influence the phase behavior of polymer blends. Xuming and Wiltzius et al. [2–4] reported that the coarsening rate of phaseseparated domains in polymer blends was greatly accelerated due to the selective wetting by substrate, leading to so-called substrate-induced phase coagulation under

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2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2005.07.021

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2-D conditions. Therefore, SALS may not be a suitable method to probe the phase boundary of binary polymer blends containing fillers, and an innovative way should be sought to examine the effect of fillers on the phase behavior of binary polymer blends. Recently, the influence of the phase behavior of binary polymer blends on the linear viscoelastic properties and, in particular, the rheology in the vicinity of phase separation has become the subject of a number of investigations [5–11]. It was observed that for temperatures in the homogeneous regime, the time–temperature superposition (TTS) principle applied well; but the TTS failed for temperatures in the two-phase region [12–17]. Moreover, for temperatures deeply into the phase-separated regime, the Han plot (logG 0 vs. logG00 ), which was suggested to be more sensitive to phase transitions [12,18], deviated from master curves [12,13,18]; and two peaks [17], or a peak with a drift tail [16] appeared also in the Cole–Cole plot (g00 vs. g 0 ). The physical origin of these behaviors was further explored by attributing it to the enhanced concentration fluctuations in the homogeneous pre-transitional region. This effect was quantified and led to the determination of the phase diagram (binodal curve [12,15,17] or both binodal and spinodal curves [13,14]) using rheological measurements. From these reports it appears that dynamic shear rheology is effective in determining the phase boundary of multicomponent polymer mixtures. Furthermore, its validity is not limited by the transparency of samples, and it probes the phase behavior under 3-D conditions, having nearly no disturbance from environment. So far, there have been few articles aimed at research related to this subject, including the determination of the phase separation temperatures of binary polymer mixtures with fillers by dynamic rheological measurements. Using rheological methods, Scherbakoff et al. [19] noted that the compatibility of an immiscible blend was improved by incorporating surface treated glass beads. However, the determination of the phase boundaries in these samples was not studied. Silva et al [20]. found that the location of thermal phase transitions, i.e., the order–order transition and order–disorder transition temperatures, as studied by small angle neutron scattering and linear viscoelastic measurements, were essentially unaffected by the incorporation of the layered silicate into polystyrene–poly(ethylene-butene-1)–polystyrene triblock (PS–PEB–PS) and PS–PEB diblock copolymers. In this paper, we systematically examined the relationship between the linear viscoelastic behavior of 5 wt.% silica particles filled poly(methyl methacrylate) (PMMA)/poly(styrene-stat-acrylonitrile) (SAN) mixtures, abbreviated as PMMA/SAN/SiO2-5, and unfilled PMMA/SAN blends, and their phase behavior, in order to extend the determination of phase boundary by dynamic shear rheology [12–15] from binary polymer

blends to ternary mixtures containing fillers; we also explored, in a preliminary way, the influence of fillers on the phase stability of binary polymer blends.

2. Experimental 2.1. Materials PMMA was obtained from LG Chemical Ltd. with Mw = 82.6 kg/mol, and Mw/Mn = 1.89. SAN was supplied by Chimei Corporation with Mw = 141 kg/mol, and Mw/Mn = 2.08. Gel permeation chromatography (GPC) with PS as the calibration standard was used to measure the molecular weight of polymers. The nitrogen content in SAN was 28.4 wt.%, which was measured by C.H.N elemental analysis. It should be noted that all the polymers used have not been further purified before use. The silica particles were synthesized by Phase Separation Co. with a nearly monodisperse size distribution and an average diameter about 6 lm. These silica particles have a specific surface area of about 250 m2/g. The surface of the silica particles had not received any treatment. All the materials were dried in a vacuum oven at 80 C for at least 24 h prior to use. 2.2. Sample preparation Blends of various compositions were prepared from ternary solutions of PMMA and SAN in 1,2-dichloroethylene at a weight fraction of 3 wt.%. First, the solvent was allowed to evaporate at room temperature for about three days. Then the samples were dried under vacuum for 24 h at 60 and 80 C, respectively. To ensure the complete removal of solvent, as judged by the constant weight, the samples continued to be dried under vacuum at 120 C (above the glass transition temperatures of the components) for two days. The films with thickness around 100 lm were cascaded and compression-molded into a specimen disk with a diameter of 25 mm and a thickness of 1 mm below 160 C and under 10 MPa for dynamic rheological measurements. 2.3. Dynamic rheological measurements A Rheometric Scientific SR-500 controlled stress rheometer was used to measure the viscoelastic properties of the blends. Parallel plates with a diameter of 25 mm were chosen. Temperature control was achieved by electrically heated plates, which had an accuracy of ±0.1 C. All measurements were carried out under N2 atmosphere to prevent any degradation and take-up of moisture. The following small amplitude oscillatory shear measurements were carried out for each blend at a fixed composition: (1) dynamic time sweeps (DTS) at a given temperature and frequency (from 0.1 to 1 rad/s), in

Y. Huang et al. / Acta Materialia 53 (2005) 5117–5124

order to obtain steady state and thus ensure that measurements were performed under ‘‘dynamic equilibrium’’ conditions; (2) dynamic stress sweeps (DSS) at a given temperature and frequency (0.1
100 rad/s), to determine the limits of linear viscoelasticity; (3) dynamic frequency sweeps (DFS) from 0.1 to 150 rad/s at a given stress, in order to determine the behavior of the storage (G 0 ) and loss (G00 ) moduli in the homogeneous, transitional, and two-phase regions. The measurement accuracy of dynamic shear rheology measurement was ±0.001 Pa.

3. Results Based on the previous work for binary polymer blends [12–17], the relationships between TTS adaptability, temperature dependence of Han plot or Cole–Cole plot and the corresponding phase behavior of PMMA/ SAN/SiO2-5 mixtures were explored. The dynamic frequency sweeps for a given composition are all plotted together in the form of master curves, obtained by shifting along the frequency axis. The master curves of G 0 and G00 for PMMA/SiO2-5 mixture are illustrated in Fig. 1(a). According to the linear viscoelastic theory, when x approaches zero, we have [6] Z þ/ G0 ðxÞjx!0 ¼ x2 H ðsÞs2 d ln s ¼ J 0e g20 x2 . ð1Þ /

Thus the slope of logG 0 vs. log aTx plots for pure PMMA should be about 2 in the terminal region. It can be seen from Fig. 1(a) that the incorporation of SiO2 particles changed the slope of plots in the terminal region to a value less than 2. However, the TTS principle still holds satisfactorily for both G 0 and G00 of PMMA/ SiO2-5 in the temperature range of the experiments, suggesting that the temperature dependence of the relaxa-

a

5119

tion behavior of PMMA molecules was not essentially influenced by the introduction of silica particles [21,22]. Theoretically, the interphase relaxation should be present in the filled polymer mixtures [23,24]. However, in the blend of PMMA/SiO2-5, only a small part of PMMA chains would be adsorbed on the surface of silica, while the majority of the PMMA chains were not under the effect of the surface force field of silica (see below). As a result, the interphase relaxation behavior is not observed in this mixture. However, in the PMMA/SAN/SiO2-5 mixture a failure of TTS for G 0 is observed in the same temperature range, as depicted in Fig. 1(b). At high frequencies the entanglement plateau is reached, while at lower frequencies the system flows in the terminal regime. It is apparent that for temperatures below 190 C the TTS applies well for both G 0 and G00 , while TTS breaks down for G 0 if the temperature is increased above 195 C, and a secondary plateau (enhanced elasticity) is present in the low frequency region. It is known that miscible polymer blends usually show a successful TTS, but it fails for phase-separated polymer mixtures [6,12–15]. This phenomenon originates from the different temperature-dependent rheology of each component in heterogeneous mixtures. The observations here are the same as reported in the binary polymer blends [6,12–15]. Thus, the failure of TTS for the temperatures above 190 C was taken as the indication that the matrix of PMMA/SAN(70/30)/ SiO2-5 mixture is phase separated. To study the phase separation rheologically, there is an alternative method suggested by Han to plot logG 0 vs. logG00 (i.e., the Han plot), where the effects of temperature and frequency are eliminated [12,13]. These curves for PMMA/SiO2-5 and PMMA/SAN(70/30)/SiO2-5 mixtures are shown in Fig. 2. As shown from Fig. 2(a), the logG 0 –logG00 curves at various temperatures could be superposed on the same master curve,

b

Fig. 1. Master curves of G 0 and G00 as a function of shifted frequency aTx, where aT is the temperature shift factor. The reference temperature is 170 C: (a) PMMA/SiO2-5; (b) PMMA/SAN(70/30)/SiO2-5 (experimental error: 0.01 dyn/cm2).

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a

b

Fig. 2. Master curves of Han plot (i.e. logG 0 vs. logG00 ): (a) PMMA/SiO2-5; (b) PMMA/SAN(70/30)/SiO2-5 (experimental error: 0.01 dyn/cm2).

that is, they show no temperature dependence. As illustrated in Fig. 2(b), for PMMA/SAN(70/30)/SiO2-5 mixture, the homogeneous phase curves coincide for 170–190 C, but the heterogeneous phase curves for 195 and 200 C deviate from them. Consequently, the result from the Han plot is well consistent with that from TTS, indicating the phase separation of polymer blends in the bulk matrix. It is known that the presence of two peaks, or under certain circumstance a peak and with drift tail in a Cole–Cole plot can be taken as signifying that the polymer mixture has undergone phase separation [17,25,41]. Such plots for PMMA/SAN/SiO2-5 mixtures were depicted in Fig. 3. It is observed that Cole–Cole plots in the phase separated regime (the curves at temperatures of 195 and 200 C) display two frequency regions, which should be caused by two different relaxation mechanisms: it was found by

Fig. 3. Cole–Cole plot for PMMA/SAN(70/30)/SiO2-5 mixture showing the occurrence of a tail beyond 195 C.

Chopra and Carreau [17,40] that at high frequencies the relaxation phenomenon is basically due to the molecular relaxation within the phase, whereas at low frequencies the relaxation mainly stems from the deformability of the suspended droplets formed by the phase separation of matrix. One can see the inception of a ‘‘tail’’ in the curve at 195 C in Fig. 3, which grows in size with a further increase in the temperature. This phenomenon has also been observed by Zheng et al. [16], Wisniewski et al. [41] and Ajji et al. [42]. The result here is exactly consistent with that reported by them. Also it is noted that the Cole–Cole plots (not shown here) for the PMMA/SiO2-5 mixture show one arc in the whole experimental temperature range. Therefore, the result from the Cole–Cole plot agrees well with that from TTS. We are unable to apply directly the analysis from TTS, the Han plot and the Cole–Cole plot for precise determination of the phase separation temperature. If the values of G 0 at the same frequency 0.1 rad/s and at various temperatures (T) are picked from Fig. 1(b) to obtain the G 0 –T curve, then the determination of phase separation temperature can be reliably realized according to the abnormal change of G 0 with T. This treatment is similar to dynamic temperature ramp (DTR) test used by other researchers [12–15,17]. The rate of temperature ramp from this treatment is virtually zero, while the real DTR test needs a certain rate of temperature increase. It should be noted that the DTR test might be ineffective in determining the phase separation temperature of filled binary polymer mixtures because of the fact that the mobility of fillers will increase with the rise of temperature, which may have an additional influence on the rheological behavior. However, DFS tests were performed here after the samples had already reached the dynamic equilibrium state, which eliminates the effect of the mobility change of fillers. Fig. 4 describes the G 0 –T curve replotted

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5121

230

105

104 TRheo=193.2oC

103

Temperature (Trheo)

G' (dyn/cm2)

225

PMMA/SAN PMMA/SAN/SiO2-5

220 215 210 205 200 195 190 185

102 165.0 170.0 175.0 180.0 185.0

190.0 195.0 200.0 205.0

T(oC)

Fig. 4. Temperature dependence of G 0 in the mixture of PMMA/ SAN(70/30)/SiO2-5 on temperature. The data are picked at 0.1 rad/s from Fig. 1(b). Trheo signifies the phase temperature determined from rheological methods. (Experimental error: 0.01 dyn/cm2.)

180 0.2

0.3

0.4

0.5

0.6

0.7

0.8

Weight Fraction of PMMA

Fig. 5. Phase diagrams of PMMA/SAN/SiO2-5 and PMMA/SAN mixtures as determined by shear rheology: Trheo. The dotted lines are obtained by the least-squares fitting for a polynomial equation.

4. Discussion from Fig. 1(b). It has been shown in Fig. 4 that at low temperatures in the homogeneous regime, an increase in temperature results in a linear decrease of G 0 due to the mobility effects associated with an increased distance from the Tg of the blend. As the temperature increases further to the vicinity of phase separation, the slope of the curve decreases, indicating that the elasticity is enhanced. This observation stems from a competition between mobility and thermodynamics [13]. The net result is an increase of G 0 because the latter force is dominant, i.e. the formation of dynamic domains rich in SAN component in the mixture. The temperature corresponding to the point that the slope of G 0 –T curve starts to decrease is referred to as the phase separation temperature of the matrix of PMMA/ SAN(70/30)/SiO2-5 mixture, that is, 193.2 C, illustrated as Trheo in Fig. 4. The phase separation temperatures of the other mixtures of various compositions are also determined using this method. The phase boundary of unfilled PMMA/SAN blend is shown in Fig. 5. The critical temperature and critical composition of the pure blend are estimated to be 184.0 C and 56% PMMA mass fraction, respectively. This result is qualitatively consistent with that reported by Ikawa et al. [26]. Also shown in Fig. 5 is the coexistence curve for the same blend with 5 wt.% of silica added. The introduction of silica particles shifts the coexistence curve vertically, relative to the pure blend, expanding the miscible region of the phase diagram. It is noted in Fig. 5 that the shift of coexistence temperature significantly depends on the blend composition. Such a shift is much larger for mixtures with PMMA as the minor component (/PMMA < 56%) than for mixtures with PMMA as the major component (/PMMA > 56%).

It may be supposed that as a result of the selective interactions of a solid filler particle surface with one component of polymer blend (preferential adsorption of one of the components), the surface layer is formed with a composition that differs from the initial composition of the blend in the bulk matrix, that is, the composition of matrix is changed correspondingly. Kalfoglou et al. [27] examined the relaxation behavior of poly (vinyl chloride) (PVC) and polyurethane (PU) in PVC/ PU/SiO2 mixtures by dynamic mechanic analysis and found that the relaxation of PU shifted to higher temperature, while that of PVC was not changed. They interpreted this result based on the acidic–basic interaction theory. There are a lot of silanol groups on the surface of SiO2 fillers, which provide acidic hydrogen atoms; and the carbonyl groups in PU provide basic oxygen atoms. As a consequence, the formation of hydrogen bonds between them has resulted in the shift of relaxation of PU molecules. However, the hydrogen bonds are absent between PVC and SiO2 because PVC is acidic too. Here, hydrogen bonds may be formed between the carbonyl groups in PMMA and silanol groups at the surface of silica particles, while no hydrogen bonds could be formed between SAN and silica due to the fact that the nitrile group in SAN is also acidic. A similar result was reported by Steinmann et al. [28], namely that glass beads selectively adsorb PMMA molecules in PMMA/PS/glass mixtures. Therefore, it may be concluded that PMMA molecules were selectively adsorbed on the surface of silica particles in the PMMA/ SAN/SiO2 mixtures. Such a selective adsorption may be responsible for the change of the phase stability of mixtures in this paper. It is interesting from our experimental work that the incorporation of SiO2 particles in

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the blend always leads to the increase in the phase separation temperature; and the change of the phase separation temperature of mixtures below the critical composition (/crit) is larger than that above the /crit, as shown in Fig. 5. These phenomena may be explained as follows: the likely adsorption of higher molecular weight fraction of PMMA on the surface of silica particles as reported by Leblanc and Stragliati [29,30] would decrease the average molecular weight of PMMA in the bulk matrix, which would favor the miscibility of PMMA/SAN blends in the matrix (as the vcrit increased), therefore leading to the increase of the phase separation temperature of blends in the bulk; In addition, the adsorption of PMMA on the surface of silica particles also decreases the PMMA fraction in the PMMA/SAN blend in the bulk matrix as compared with unfilled blends. It would also increase the phase separation temperature if the changed blend composition ratio in the bulk matrix is below the critical composition (/crit = 56%, as shown in Fig. 5, see the unfilled blend curve), or decrease the phase separation temperature if it is located above the critical composition /crit. The synergistic operation of the above two factors may result in an increase in the phase separation temperature by a noticeable magnitude. However, more experimental work is required before a definite conclusion can be drawn. Additionally, the phase behavior of the filled and unfilled PMMA/SAN mixtures was modeled using FloryÕs statistical mechanical model [31]. It is assumed that the Flory–Huggins interaction parameter, v, depends on temperature alone, conforming to the relation v = A  B/T [17]. The fitted values of A and B were used to estimate the temperature dependence of v. By using the Flory–Huggins theory, according to which, at equilibrium, the following two equations arise from the equality of the chemical potentials of component 1 and component 2 in both phases v1 ¼ v2 ¼

lnðu01 =u001 Þ

þ ð1  r1 =r2 Þðu02 02 r1 ðu002 2  u2 Þ lnðu02 =u002 Þ þ ð1  r2 =r1 Þðu01 02 r2 ðu002 1  u1 Þ

u002 Þ

;

ð2Þ

 u001 Þ

.

ð3Þ



In theory, Eqs. (2) and (3) should yield the same result, that is, v1 = v2. It is assumed here that v ¼ ðv1 þ v2 Þ=2.

ð4Þ

Eqs. (2) and (3) have been successfully used by Friedrich et al. [32] to calculate the v parameter for binary poly-

mer blends, and Eq. (4) has been used by Nesterov et al. [33] for polymer/polymer/filler ternary mixtures. ui (i = 1, 2) are the volume fractions of the components, which are calculated from the weight fractions at equilibrium obtained from the phase diagram (Fig. 5) assuming a vanishing excess mixing volume. The ri is the number of segments of per chain, which are calculated using the equation ri = PiVi(V1V2)1/2, where Pi is the number average degree of polymerization and Vi the monomer volume of the component i. As stated previously, the selective adsorption will result in the composition change of matrix. This effect should be considered when calculating the ui. As far as the silica-polysiloxane mixtures were concerned, Cohen-Addad [34,35] submitted theoretical developments for systems where the mechanism of polymer adsorption on filler particles is well identified as the formation of hydrogen bonds between oxygen atoms on polymer chains and silanol groups located on silica surface. By considering that polysiloxane chains obey Gaussian statistics, Cohen-Addad derived the following relationship for the weight fraction of the bound rubber, wBdR, i.e. pffiffiffiffiffiffiffi  0 cS pffiffiffiffiffiffiffi M  n; M ð5Þ wBdR ¼ A0 ea N AV  0 is the average weight of one skeletal bond where M (equal to 37 g mol1 for siloxane), A0 the average area (on the filler particle) associated with one hydrogen bond (equal to 0.55 nm2 for silanol group), ea  1 a numerical factor accounting for chain stiffness and sur n the number average molecular weight face coverage, M for the polymer, c the filler concentration (g/g of polymer), S the specific area of filler (m2/g), and NAV the Avogadro number (6.023 · 1023 mol1). After the incorporation of silica particles, the composition change will abide by the following relation: wPMMA ¼ ð1  wBdR Þw0PMMA ;

ð6Þ

where wPMMA, w0PMMA are the weight fractions of PMMA in the matrix after and before the introduction of silica fillers, respectively. Table 1 presents an example of the component ratios and interaction parameters in separated phases of unfilled and filled PMMA/SAN mixtures at the same temperature 200 C. As can be seen from Table 1, the mass fraction of PMMA in SAN-enriched phase is much higher than that of SAN in PMMA-enriched phase, which means that PMMA has better solubility in SAN

Table 1 The calculated component ratios and interaction parameters in separated phases of unfilled and filled PMMA/SAN mixtures at 200 C according to the phase diagram in Fig. 5 Mixture

PMMA-enriched phase u01 ,

Unfilled Filled

PMMA

0.830 0.722

v (103)

SAN-enriched phase u02 ,

SAN

0.170 0.278

u001 ,

PMMA

0.255 0.295

u002 ,

SAN

0.745 0.705

3.85 3.66

Y. Huang et al. / Acta Materialia 53 (2005) 5117–5124

as compared to that of SAN in PMMA. Of great interest is the fact that for the filled mixtures, the solubilities of both PMMA in SAN-enriched phase and of SAN in PMMA-enriched phase are much higher than those of unfilled mixtures. These results show that the silica particles improve the solubility of one component in another, that is, improve their miscibility, which is in accordance with the result of the parameter v (see below). The change of the composition of the mixture matrix, which is not exposed to the filler action, changes the phase composition during phase separation. From the results in Table 1, the parameter v for the filled mixture is lower than that for the unfilled mixture. In addition, the temperature dependence of v for PMMA/SAN blend is depicted in Fig. 6, abiding by the relation of v(T) = 0.0176.442/T. The v parameter at room temperature 25 C calculated according to this relation gave 0.0046. The result is consistent with the value, v P 0.01, which was determined using SANS by other researchers [36,37]. The temperature dependence of v for PMMA/SAN/SiO2-5 mixture is also illustrated in Fig. 6, which can be expressed in the same form as v(T) = 0.014  5.024/T. As can be seen from Fig. 6, the Flory–Huggins interaction parameter of the filled blend is reduced in the experimental temperature range compared with the unfilled one at the same temperature condition, suggesting that the thermodynamic stability or miscibility of the mixture is enhanced due to the introduction of the silica particles. In fact, the filled mixture can be considered as a ternary system with specific interactions among components A and B with the functional groups at the filler surface (denoted as S). Nesterov et al.[38] developed a thermodynamic equation for such systems based on the Flory–Huggins mean field theory, but they believed that all the polymer chains interact with fillers. However, in fact only the chains at the surface layer have

5123

the opportunity to interact with fillers, while it would be very difficult for the chains within the mixture matrix to interact with fillers. We have further developed the thermodynamic equations for such a ternary mixture, where the surface layer and matrix coexists [39]. The effective Flory–Huggins interaction parameter can be expressed as SL SL SL M M vfil ¼ vAS uSL A uS þ vBS uB uS þ vAB ðuA uB þ uA uB Þ;

ð7Þ where viS is the parameter of thermodynamic interaction of ith polymer component with functional groups at the filler surface; uS and uSL i are the volume fractions of the active groups and ith polymer component in the surface layer, respectively; uM i is the volume fraction of ith polymer component in the matrix; and vAB is the thermodynamic interaction parameter between polymer A and polymer B. For PMMA/SAN/SiO2-5 mixture, the surface layer can be regarded as being formed by only PMMA chains because silica particles selectively adsorb PMMA chains (viz. uSL B ¼ 0Þ. Thus, Eq. (7) is reduced to M M vfil ¼ vAS uSL A uS þ vAB uA uB .

ð8Þ

It should be noted that this equation does not take into account the fact that in the surface layers the very value of vAB may differ from the same value in the bulk. If the value of vAS is negative, vfil will be less than vAB, that is, the mixture becomes thermodynamically more stable in the presence of a filler. Because of this, one can also expect that for the lower critical solution temperature system, the temperature of phase separation of the matrix of filled mixtures will be higher than that of unfilled mixtures. The increase in the phase separation temperature due to the incorporation of filler was confirmed experimentally (Fig. 5). 5. Conclusions

0.0042 0.0041 0.0040

χ

0.0039 0.0038 0.0037 0.0036 0.0035

PMMA/SAN PMMA/SAN/SiO2

0.0034

Least-square fitting

0.0033 2.00 2.02 2.04 2.06 2.08 2.10 2.12 2.14 2.16 2.18 2.20 3 -1

1/T (10 K )

Fig. 6. The temperature dependence of v for PMMA/SAN and PMMA/SAN/SiO2-5 mixtures. Dotted lines were obtained by the least-squares fitting for the equation of v = A  B/T.

The determination of phase separation temperature by dynamic shear rheology can be extended from binary polymer blends to ternary mixtures composed of two polymers and one filler. Preliminary measurements and calculation show that the phase separation temperature of a PMMA/SAN blend is increased and the thermodynamic interaction parameter is decreased due to the introduction of silica filler, suggesting that the phase stability of PMMA/ SAN mixtures is enhanced by the incorporation of silica. A possible mechanism for this phenomenon has been proposed based on the selective adsorption of high molecular weight PMMA chains on the surface of silica particles. However, more experimental work is required before a definite conclusion can be drawn. Future studies should be concentrated on the role of particle shape, dispersion, size and content on the phase boundary and

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phase separation dynamics. This will require precise control of the surface chemistry of fillers and density of active sites.

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